Background

This analysis document compliments FIA NLS Models: Biomass vs. Stand Age. All of the background information from that document applies to these analyses, which are extensions to them. In this analysis, we fit models to the temporally-balanced dataset, which uses the first and most-recent plot re-measurement for each FIA plot. Then, we conduct a model bookeeping analysis, which does biomass change attribution to:

  1. age-related biomass change
  2. productivity-trend driven biomass change
  3. disturbance regime (changes in the biomass loss rate)- attributable biomass change

Below the model fitting procedure is implemented by ecoprovince:

Using temporally-balanced data

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4834     1203.6                                
## 2   4833     1092.6  1 111.05  491.22 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 52557.62
## 2     2 52091.41
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.45951    0.16992   2.704  0.00687 ** 
## alpha   0.84855    0.03503  24.221  < 2e-16 ***
## A     473.76484   37.00356  12.803  < 2e-16 ***
## k     205.69316   18.21698  11.291  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4755 on 4833 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.017e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) : 
##   object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) : 
##   object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) : 
##   object 'Mod.Sel3' not found
##   model      AIC
## 1     2 52091.41
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.45951    0.16992   2.704  0.00687 ** 
## alpha   0.84855    0.03503  24.221  < 2e-16 ***
## A     473.76484   37.00356  12.803  < 2e-16 ***
## k     205.69316   18.21698  11.291  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4755 on 4833 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.017e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4832     1179.6                                
## 2   4831     1067.7  1 111.87  506.17 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 52091.41
## 2     4 52463.90
## 3     5 51983.93
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.58118    0.17752   3.274  0.00107 ** 
## alpha   0.84078    0.03411  24.646  < 2e-16 ***
## a      33.40070    1.99286  16.760  < 2e-16 ***
## b     118.88478    5.92661  20.059  < 2e-16 ***
## c     118.37512    5.85956  20.202  < 2e-16 ***
## d       1.01653    0.05233  19.425  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4701 on 4831 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12943     5165.4                                
## 2  12942     5044.1  1 121.33   311.3 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 135621.4
## 2     2 135315.7
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.95237    0.12759   7.464 8.91e-14 ***
## alpha   0.62169    0.03318  18.736  < 2e-16 ***
## A     165.96924    5.63575  29.449  < 2e-16 ***
## k      78.87707    3.15407  25.008  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6243 on 12942 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 8.623e-06
##   (16 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12942     5044.1                                
## 2  12941     5021.8  1 22.266  57.378 3.839e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 135315.7
## 2    2a 135260.4
## 3    2b 135317.6
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   9.238e-01  1.259e-01   7.336 2.33e-13 ***
## alpha 6.214e-01  3.094e-02  20.082  < 2e-16 ***
## A     1.921e+02  9.346e+00  20.559  < 2e-16 ***
## k     1.085e+02  7.979e+00  13.593  < 2e-16 ***
## p     2.121e-02  2.492e-03   8.509  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6229 on 12941 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.063e-06
##   (16 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12941     5088.9                                
## 2  12940     4912.4  1 176.51  464.95 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 135260.4
## 2     4 135432.3
## 3     5 134977.3
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.19051    0.13607   8.749   <2e-16 ***
## alpha   0.67333    0.02702  24.922   <2e-16 ***
## a      13.38590    0.51341  26.073   <2e-16 ***
## b      75.80154    2.36631  32.034   <2e-16 ***
## c     121.05709    5.45544  22.190   <2e-16 ***
## d       1.41595    0.04287  33.030   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6161 on 12940 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (16 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5442     948.80                                
## 2   5441     857.87  1 90.926  576.69 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 59550.63
## 2     2 59004.09
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.1644     0.1261   1.304    0.192    
## alpha   0.8050     0.0312  25.799   <2e-16 ***
## A     500.5614    30.8115  16.246   <2e-16 ***
## k     155.6108    11.1725  13.928   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3971 on 5441 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.272e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)   
## 1   5441     857.87                             
## 2   5440     856.53  1 1.3429   8.529 0.00351 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 59004.09
## 2    2a 58997.56
## 3    2b 58973.93
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.23383    0.13009   1.797   0.0723 .  
## alpha   0.81624    0.03142  25.975   <2e-16 ***
## A     293.53650   21.44552  13.688   <2e-16 ***
## k      64.20469    6.41740  10.005   <2e-16 ***
## s       1.31952    0.05962  22.132   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3959 on 5440 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.275e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5440     940.37                                
## 2   5439     848.31  1 92.062  590.26 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 58973.93
## 2     4 59506.03
## 3     5 58947.03
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.24222    0.13018   1.861   0.0629 .  
## alpha   0.80822    0.03087  26.178  < 2e-16 ***
## a      21.08256    2.67854   7.871 4.22e-15 ***
## b     179.51639   10.45102  17.177  < 2e-16 ***
## c     156.83930   15.71326   9.981  < 2e-16 ***
## d       1.51879    0.08979  16.915  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3949 on 5439 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3547     1178.6                                
## 2   3546     1136.5  1 42.068  131.25 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 38157.03
## 2     2 38030.00
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.03509    0.24350   4.251 2.18e-05 ***
## alpha   0.72686    0.05912  12.295  < 2e-16 ***
## A     445.56009   55.43529   8.037 1.24e-15 ***
## k     254.71684   34.82136   7.315 3.17e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5661 on 3546 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.413e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)    
## 1   3546     1136.5                              
## 2   3545     1132.9  1 3.5914  11.238 0.00081 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 38030.00
## 2    2a 38020.77
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau     1.091545   0.248065   4.400 1.11e-05 ***
## alpha   0.753308   0.059393  12.683  < 2e-16 ***
## A     342.271688  43.589966   7.852 5.38e-15 ***
## k     170.045425  28.883552   5.887 4.29e-09 ***
## p      -0.015140   0.006514  -2.324   0.0202 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5653 on 3545 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 5.957e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3545     1160.1                                
## 2   3544     1108.8  1 51.282  163.91 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 38020.77
## 2     4 38104.80
## 3     5 37946.29
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.21145    0.25520   4.747 2.14e-06 ***
## alpha   0.76881    0.05439  14.134  < 2e-16 ***
## a      14.01898    1.39169  10.073  < 2e-16 ***
## b     101.92211    6.02465  16.918  < 2e-16 ***
## c     115.56990    8.21593  14.067  < 2e-16 ***
## d       1.19701    0.06667  17.955  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5593 on 3544 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6383     1208.6                                
## 2   6382     1143.1  1 65.521  365.81 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 66739.63
## 2     2 66385.70
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.80821    0.12030   6.718    2e-11 ***
## alpha   0.70093    0.03432  20.426   <2e-16 ***
## A     212.97304    8.46135  25.170   <2e-16 ***
## k      72.75583    3.94421  18.446   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4232 on 6382 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.25e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6382     1143.1                                
## 2   6381     1142.5  1 0.6350  3.5469    0.0597 .  
## 3   6381     1136.2  0 0.0000                      
## 4   6380     1128.1  1 8.1539 46.1159 1.215e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 66385.70
## 2    2a 66384.15
## 3    2b 66349.16
## 4    2c 66305.16
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.85759    0.12173   7.045 2.05e-12 ***
## alpha   0.71209    0.03381  21.062  < 2e-16 ***
## A     127.11413    4.61707  27.531  < 2e-16 ***
## k      37.02397    1.25609  29.475  < 2e-16 ***
## p       0.14094    0.01883   7.486 8.09e-14 ***
## s       2.17271    0.15279  14.220  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4205 on 6380 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.063e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6381     1195.9                                
## 2   6380     1127.7  1 68.139   385.5 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 66305.16
## 2     4 66675.81
## 3     5 66303.16
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.84613    0.12109   6.988 3.08e-12 ***
## alpha   0.71122    0.03383  21.023  < 2e-16 ***
## a      17.80094    2.07031   8.598  < 2e-16 ***
## b      98.51432    3.90582  25.222  < 2e-16 ***
## c     113.18502    6.98395  16.206  < 2e-16 ***
## d       1.44570    0.07453  19.398  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4204 on 6380 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7773     2698.5                                
## 2   7772     2568.4  1 130.03  393.48 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 85845.56
## 2     2 85463.52
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.24476    0.17019   7.314 2.86e-13 ***
## alpha   0.57095    0.02662  21.444  < 2e-16 ***
## A     257.12975   11.27279  22.810  < 2e-16 ***
## k      67.16853    3.01370  22.288  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5749 on 7772 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.572e-06
##   (14 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7772     2568.4                                
## 2   7771     2545.5  1 22.931  70.004 < 2.2e-16 ***
## 3   7771     2566.4  0  0.000                      
## 4   7770     2496.6  1 69.841 217.364 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 85463.52
## 2    2a 85395.79
## 3    2b 85459.40
## 4    2c 85246.85
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   1.506e+00  1.836e-01   8.201 2.76e-16 ***
## alpha 6.512e-01  2.258e-02  28.840  < 2e-16 ***
## A     1.450e+02  6.248e+00  23.205  < 2e-16 ***
## k     3.016e+01  1.222e+00  24.686  < 2e-16 ***
## p     1.076e-01  7.674e-03  14.024  < 2e-16 ***
## s     1.963e+00  9.744e-02  20.143  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5668 on 7770 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 5.033e-06
##   (14 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7771     2669.8                                
## 2   7770     2494.5  1 175.36  546.22 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 85246.85
## 2     4 85766.57
## 3     5 85240.29
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.47599    0.18195   8.112 5.75e-16 ***
## alpha   0.65085    0.02255  28.860  < 2e-16 ***
## a      16.12785    0.82771  19.485  < 2e-16 ***
## b     120.36292    5.58045  21.569  < 2e-16 ***
## c     112.83900    9.26790  12.175  < 2e-16 ***
## d       1.63350    0.06625  24.657  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5666 on 7770 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (14 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7905     4072.2                                
## 2   7904     3928.6  1 143.61  288.94 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 88878.43
## 2     2 88596.51
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.76811    0.18004   4.266 2.01e-05 ***
## alpha   0.55314    0.02987  18.521  < 2e-16 ***
## A     270.07655   14.26944  18.927  < 2e-16 ***
## k      71.69928    3.93397  18.226  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.705 on 7904 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.137e-06
##   (32 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7904     3928.6                                
## 2   7903     3859.0  1 69.597  142.53 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 88596.51
## 2    2a 88457.16
## 3    2b 88567.74
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   9.272e-01  1.885e-01   4.920 8.85e-07 ***
## alpha 6.432e-01  2.456e-02  26.191  < 2e-16 ***
## A     4.083e+02  4.091e+01   9.981  < 2e-16 ***
## k     1.596e+02  2.131e+01   7.489 7.67e-14 ***
## p     2.506e-02  1.901e-03  13.185  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6988 on 7903 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.089e-06
##   (32 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7903     4029.5                                
## 2   7902     3773.8  1 255.69  535.39 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 88457.16
## 2     4 88799.14
## 3     5 88282.71
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.00852    0.19081   5.285 1.29e-07 ***
## alpha   0.71043    0.02138  33.233  < 2e-16 ***
## a      20.51866    1.02371  20.043  < 2e-16 ***
## b     121.27486    6.30094  19.247  < 2e-16 ***
## c     111.11452    9.25971  12.000  < 2e-16 ***
## d       1.50283    0.06832  21.998  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6911 on 7902 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (32 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    826     218.04                                
## 2    825     194.59  1 23.448  99.412 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9094.121
## 2     2 9001.802
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   3.865e-01  4.112e-01   0.940   0.3476    
## alpha 7.628e-01  6.984e-02  10.922   <2e-16 ***
## A     1.255e+03  5.318e+02   2.360   0.0185 *  
## k     4.893e+02  2.232e+02   2.192   0.0286 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4857 on 825 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.631e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_234,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    825     194.59                            
## 2    823     192.48  2 2.1059  4.5022 0.01136 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 9001.802
## 2    2a       NA
## 3    2b       NA
## 4    2c 8996.781
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.39536    0.41113   0.962    0.337    
## alpha   0.78925    0.07021  11.242  < 2e-16 ***
## A     395.47217  189.29921   2.089    0.037 *  
## k      99.96670   70.69953   1.414    0.158    
## p      -0.01220    0.01423  -0.857    0.392    
## s       1.13109    0.24438   4.628 4.28e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4836 on 823 degrees of freedom
## 
## Number of iterations to convergence: 40 
## Achieved convergence tolerance: 3.1e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    824     216.69                                
## 2    823     192.29  1 24.399  104.43 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 8996.781
## 2     4 9092.966
## 3     5 8995.935
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.4024     0.4120   0.977  0.32908    
## alpha   0.7883     0.0701  11.246  < 2e-16 ***
## a       0.0000     5.9324   0.000  1.00000    
## b     340.8238   204.3728   1.668  0.09576 .  
## c     675.4071   940.5067   0.718  0.47288    
## d       2.5547     0.6884   3.711  0.00022 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4834 on 823 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1387     347.56                                
## 2   1386     336.63  1 10.934   45.02 2.834e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14526.30
## 2     2 14483.87
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.28977    0.25193   1.150     0.25    
## alpha   0.68210    0.09544   7.147 1.43e-12 ***
## A     261.45525   28.66195   9.122  < 2e-16 ***
## k     106.87482   14.79744   7.223 8.39e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4928 on 1386 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 9.101e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1   1386     336.63                             
## 2   1385     336.63  1 5.7789e-05   2e-04 0.9877
##   model      AIC
## 1     2 14483.87
## 2    2a 14485.87
## 3    2b 14469.11
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.34766    0.25540   1.361    0.174    
## alpha   0.70227    0.09501   7.391 2.51e-13 ***
## A     142.90894   13.48623  10.597  < 2e-16 ***
## k      39.02880    3.98802   9.787  < 2e-16 ***
## s       1.74387    0.18179   9.593  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.49 on 1385 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 6.83e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1385     337.23                                
## 2   1384     325.82  1 11.409  48.464 5.181e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 14469.11
## 2     4 14488.37
## 3     5 14442.53
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.34162    0.25201   1.356    0.175    
## alpha   0.70124    0.09431   7.435 1.82e-13 ***
## a      24.39435    4.05270   6.019 2.24e-09 ***
## b      93.28179    7.41989  12.572  < 2e-16 ***
## c     102.73710    8.92197  11.515  < 2e-16 ***
## d       1.13595    0.10865  10.455  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4852 on 1384 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    439     237.09                            
## 2    438     235.09  1 2.0089  3.7429 0.05368 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4609.958
## 2     2 4608.197
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau    -0.1340     0.6019  -0.223  0.82393   
## alpha   0.3504     0.1744   2.009  0.04512 * 
## A     320.3752   106.7015   3.003  0.00283 **
## k     143.2259    52.7209   2.717  0.00686 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7326 on 438 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.634e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    438     235.09                         
## 2    437     234.74  1 0.3499  0.6514 0.4201
##   model      AIC
## 1     2 4608.197
## 2    2a 4609.539
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau    -0.1340     0.6019  -0.223  0.82393   
## alpha   0.3504     0.1744   2.009  0.04512 * 
## A     320.3752   106.7015   3.003  0.00283 **
## k     143.2259    52.7209   2.717  0.00686 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7326 on 438 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.634e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    437     226.64                              
## 2    436     221.69  1 4.9467  9.7286 0.001934 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 4608.197
## 2     4 4594.028
## 3     5 4586.274
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.2440     0.5501  -0.443 0.657650    
## alpha   0.5283     0.1577   3.350 0.000877 ***
## a       9.5645     1.9483   4.909 1.30e-06 ***
## b      88.5138    12.4743   7.096 5.24e-12 ***
## c      55.9913     5.9220   9.455  < 2e-16 ***
## d       1.0392     0.1138   9.129  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7131 on 436 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (only 64 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (0 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_322.", Mod.Sel1, sep = "")) : 
##   object 'nls_322.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model
  • not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)   
## 1    149     87.775                             
## 2    148     83.201  1 4.5741  8.1365 0.00496 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1640.707
## 2     2 1634.572
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau     3.0055     4.1286   0.728  0.46779   
## alpha   0.9714     0.2977   3.263  0.00137 **
## A     231.9254   226.9888   1.022  0.30857   
## k     219.8242   199.9830   1.099  0.27346   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7498 on 148 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.357e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    148     83.201                           
## 2    147     83.108  1 0.093179  0.1648 0.6854
##   model      AIC
## 1     2 1634.572
## 2    2a       NA
## 3    2b 1636.402
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau     3.0055     4.1286   0.728  0.46779   
## alpha   0.9714     0.2977   3.263  0.00137 **
## A     231.9254   226.9888   1.022  0.30857   
## k     219.8242   199.9830   1.099  0.27346   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7498 on 148 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.357e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Error in nls(f_5, data = G_332, start = c(tau = tau.start, alpha = alpha.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model      AIC
## 1     2 1634.572
## 2     4 1636.879
## 3     5       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau     3.0055     4.1286   0.728  0.46779   
## alpha   0.9714     0.2977   3.263  0.00137 **
## A     231.9254   226.9888   1.022  0.30857   
## k     219.8242   199.9830   1.099  0.27346   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7498 on 148 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.357e-06
##   (2 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: does not fit

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit

  • log-normal phi model: does not fit

  • model not fitted because only 62 observations

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5103     963.25                                
## 2   5102     841.07  1 122.19  741.21 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 54262.24
## 2     2 53571.63
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.63454    0.16362   3.878 0.000107 ***
## alpha   0.80068    0.02686  29.811  < 2e-16 ***
## A     446.29921   29.09383  15.340  < 2e-16 ***
## k     198.11601   13.75314  14.405  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.406 on 5102 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.889e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5102     841.07                                
## 2   5101     833.07  1 8.0008   48.99 2.905e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 53571.63
## 2    2a 53524.82
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.51537    0.15576   3.309 0.000944 ***
## alpha   0.81328    0.02703  30.083  < 2e-16 ***
## A     324.77328   20.26162  16.029  < 2e-16 ***
## k     102.66625   10.74934   9.551  < 2e-16 ***
## p      -0.05130    0.01127  -4.551 5.47e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4041 on 5101 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.641e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5101     952.58                                
## 2   5100     828.03  1 124.55  767.12 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 53524.82
## 2     4 54209.36
## 3     5 53495.89
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.53028    0.15658   3.387 0.000713 ***
## alpha   0.81390    0.02671  30.470  < 2e-16 ***
## a      14.56503    2.98921   4.873 1.14e-06 ***
## b     155.65092   10.10200  15.408  < 2e-16 ***
## c     179.79825   19.79447   9.083  < 2e-16 ***
## d       1.58647    0.10396  15.261  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4029 on 5100 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5180     879.40                                
## 2   5179     824.61  1  54.79  344.11 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 57351.18
## 2     2 57019.77
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.69968    0.13285   5.267 1.45e-07 ***
## alpha   0.82371    0.04201  19.609  < 2e-16 ***
## A     266.46784   10.04611  26.524  < 2e-16 ***
## k      61.97132    3.14535  19.703  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.399 on 5179 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.081e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)    
## 1   5179     824.61                               
## 2   5178     823.80  1  0.8171  5.1361 0.02347 *  
## 3   5178     817.30  0  0.0000                    
## 4   5177     805.02  1 12.2794 78.9674 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 57019.77
## 2    2a 57016.63
## 3    2b 56975.59
## 4    2c 56899.12
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.87739    0.14139   6.206 5.87e-10 ***
## alpha   0.82469    0.03959  20.832  < 2e-16 ***
## A     162.45200    5.61416  28.936  < 2e-16 ***
## k      37.03352    1.05271  35.179  < 2e-16 ***
## p       0.20173    0.01784  11.310  < 2e-16 ***
## s       2.64792    0.19044  13.904  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3943 on 5177 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.479e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5178     862.65                                
## 2   5177     803.67  1 58.977  379.91 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 56899.12
## 2     4 57255.49
## 3     5 56890.45
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.87572    0.14097   6.212 5.64e-10 ***
## alpha   0.82430    0.03969  20.766  < 2e-16 ***
## a      31.76130    2.62008  12.122  < 2e-16 ***
## b     122.35089    4.61204  26.529  < 2e-16 ***
## c     103.12833    4.07801  25.289  < 2e-16 ***
## d       1.27367    0.05860  21.735  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.394 on 5177 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    596     80.866                                
## 2    595     71.900  1 8.9663    74.2 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6115.535
## 2     2 6047.140
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.07855    0.26298  -0.299    0.765    
## alpha   0.89957    0.09748   9.228  < 2e-16 ***
## A     298.68647   41.73938   7.156 2.45e-12 ***
## k      95.82372   18.87728   5.076 5.16e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3476 on 595 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.77e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    595     71.900                          
## 2    594     71.708  1 0.19119  1.5837 0.2087
##   model      AIC
## 1     2 6047.140
## 2    2a 6047.545
## 3    2b 6048.497
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.07855    0.26298  -0.299    0.765    
## alpha   0.89957    0.09748   9.228  < 2e-16 ***
## A     298.68647   41.73938   7.156 2.45e-12 ***
## k      95.82372   18.87728   5.076 5.16e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3476 on 595 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.77e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    594     80.723                                
## 2    593     71.768  1 8.9544  73.988 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 6047.140
## 2     4 6118.473
## 3     5 6050.044
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.07855    0.26298  -0.299    0.765    
## alpha   0.89957    0.09748   9.228  < 2e-16 ***
## A     298.68647   41.73938   7.156 2.45e-12 ***
## k      95.82372   18.87728   5.076 5.16e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3476 on 595 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.77e-06
##   (3 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    676     152.77                                
## 2    675     142.27  1 10.498  49.809 4.216e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7025.553
## 2     2 6979.211
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5697     0.5042   1.130    0.259    
## alpha   0.8583     0.1139   7.536 1.57e-13 ***
## A     315.8268    62.8438   5.026 6.44e-07 ***
## k     147.8427    33.1149   4.465 9.40e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4591 on 675 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.062e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1    675     142.27                            
## 2    674     142.26  1 0.0098593  0.0467 0.8290
## 3    674     142.26  0 0.0000000               
## 4    673     142.26  1 0.0069224  0.0327 0.8564
##   model      AIC
## 1     2 6979.211
## 2    2a 6981.164
## 3    2b 6981.181
## 4    2c 6983.148
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5697     0.5042   1.130    0.259    
## alpha   0.8583     0.1139   7.536 1.57e-13 ***
## A     315.8268    62.8438   5.026 6.44e-07 ***
## k     147.8427    33.1149   4.465 9.40e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4591 on 675 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.062e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Error in nls(f_5, data = G_M231, start = c(tau = tau.start, alpha = alpha.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model      AIC
## 1     2 6979.211
## 2     4 7029.273
## 3     5       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5697     0.5042   1.130    0.259    
## alpha   0.8583     0.1139   7.536 1.57e-13 ***
## A     315.8268    62.8438   5.026 6.44e-07 ***
## k     147.8427    33.1149   4.465 9.40e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4591 on 675 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.062e-06
##   (1 observation deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: does not fit

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    326    100.337                            
## 2    325     98.647  1 1.6905  5.5696 0.01887 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3504.259
## 2     2 3500.669
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.5690     1.1894   1.319  0.18805    
## alpha   0.6751     0.2661   2.537  0.01165 *  
## A      85.0151    18.2427   4.660 4.61e-06 ***
## k      22.9171     7.8626   2.915  0.00381 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5509 on 325 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.882e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)  
## 1    325     98.647                            
## 2    324     97.539  1 1.10741  3.6785 0.0560 .
## 3    324     93.712  0 0.00000                 
## 4    323     93.308  1 0.40411  1.3989 0.2378  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 3500.669
## 2    2a 3498.954
## 3    2b 3485.785
## 4    2c 3486.363
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.8945     1.2923   1.466   0.1436    
## alpha   0.6580     0.2763   2.381   0.0178 *  
## A      65.9248    13.3842   4.926 1.34e-06 ***
## k      30.8188     3.7464   8.226 4.75e-15 ***
## s      42.5340   187.7406   0.227   0.8209    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5378 on 324 degrees of freedom
## 
## Number of iterations to convergence: 21 
## Achieved convergence tolerance: 8.771e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    324     96.856                            
## 2    323     95.476  1   1.38  4.6688 0.03145 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 3485.785
## 2     4 3496.641
## 3     5 3493.920
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.8945     1.2923   1.466   0.1436    
## alpha   0.6580     0.2763   2.381   0.0178 *  
## A      65.9248    13.3842   4.926 1.34e-06 ***
## k      30.8188     3.7464   8.226 4.75e-15 ***
## s      42.5340   187.7406   0.227   0.8209    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5378 on 324 degrees of freedom
## 
## Number of iterations to convergence: 21 
## Achieved convergence tolerance: 8.771e-06
##   (1 observation deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit

  • log-normal phi model: does not fit

  • model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    299     124.35                                
## 2    298     113.37  1 10.974  28.846 1.581e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3013.807
## 2     2 2987.903
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.07662    0.66159   0.116  0.90788    
## alpha  0.77829    0.12977   5.998 5.79e-09 ***
## A     99.54181   19.23214   5.176 4.18e-07 ***
## k     53.05797   17.65911   3.005  0.00289 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6168 on 298 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.942e-06
##   (4 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    298     113.37                           
## 2    297     113.26  1 0.115630  0.3032 0.5823
## 3    297     113.00  0 0.000000               
## 4    296     112.91  1 0.094618  0.2480 0.6188
##   model      AIC
## 1     2 2987.903
## 2    2a 2989.595
## 3    2b 2988.916
## 4    2c 2990.663
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df_bal$Ecoprovince == "M334", :
## provided 33 variables to replace 32 variables
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.07662    0.66159   0.116  0.90788    
## alpha  0.77829    0.12977   5.998 5.79e-09 ***
## A     99.54181   19.23214   5.176 4.18e-07 ***
## k     53.05797   17.65911   3.005  0.00289 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6168 on 298 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.942e-06
##   (4 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    297     124.07                                
## 2    296     113.29  1 10.775  28.151 2.203e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 2987.903
## 2     4 3017.126
## 3     5 2991.690
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.07662    0.66159   0.116  0.90788    
## alpha  0.77829    0.12977   5.998 5.79e-09 ***
## A     99.54181   19.23214   5.176 4.18e-07 ***
## k     53.05797   17.65911   3.005  0.00289 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6168 on 298 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.942e-06
##   (4 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Ecoprovince Ecoregion Sel.Mod.2 Sel.Mod.3 Best.Mod
211 Northeastern Mixed Forest 2 5 5
212 Laurentian Mixed Forest 2a 5 5
221 Eastern Broadleaf Forest 2b 5 5
222 Midwest Broadleaf Forest 2a 5 5
223 Central Interior Broadleaf Forest 2c 5 5
231 Southeastern Mixed Forest 2c 5 5
232 Outer Coastal Plain Mixed Forest 2a 5 5
234 Lower Mississippi Riverine Forest 2c 5 5
242 Pacific Lowland Mixed Forest NA NA NA
251 Prairie Parkland (Temperate) 2b 5 5
255 Prairie Parkland (Subtropical) 2 5 5
261 California Coastal Chaparral Forest and Shrub NA NA NA
262 California Dry Steppe NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA NA NA
313 Colorado Plateau Semi-Desert NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA NA NA
321 Chihuahuan Semi-Desert NA NA NA
322 American Semidesert and Desert NA NA NA
331 Great Plains/Palouse Dry Steppe NA NA NA
332 Great Plains Steppe 2 2 2
341 Intermountain Semi-Desert and Desert NA NA NA
342 Intermountain Semi-Desert NA NA NA
411 Everglades NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2a 5 5
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2c 5 5
M223 Ozark Broadleaf Forest Meadow 2 2 2
M231 Ouachita Mixed Forest 2 2 2
M242 Cascade Mixed Forest NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2b 2b 2b
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA NA NA
M334 Black Hills Coniferous Forest 2 2 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA NA NA

table by ecoprovince

Ecoprovince Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5 a a.2.5 a.97.5 b b.se b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 4838 2419 0.5811807 0.0315130 0.2331627 0.9291986 0.8407842 0.0011638 0.7739056 0.9076629 473.76484 401.22103 546.30865 205.69316 169.97959 241.40674 33.400705 29.493797 37.30761 118.88478 NA 107.26593 130.50363 118.37512 106.88772 129.86252 1.016528 0.9139327 1.119122
212 Laurentian Mixed Forest east 12962 6481 1.1905141 0.0185145 0.9238008 1.4572274 0.6733287 0.0007299 0.6203705 0.7262870 192.14309 173.82377 210.46242 108.46141 92.82129 124.10153 13.385905 12.379552 14.39226 75.80154 NA 71.16321 80.43987 121.05709 110.36363 131.75055 1.415947 1.3319180 1.499977
221 Eastern Broadleaf Forest east 5446 2723 0.2422230 0.0169479 -0.0129899 0.4974359 0.8082238 0.0009532 0.7476984 0.8687492 293.53650 251.49470 335.57830 64.20469 51.62403 76.78536 21.082556 15.831554 26.33356 179.51639 NA 159.02822 200.00457 156.83930 126.03502 187.64358 1.518786 1.3427586 1.694814
222 Midwest Broadleaf Forest east 3552 1776 1.2114537 0.0651252 0.7111070 1.7118003 0.7688102 0.0029588 0.6621620 0.8754583 342.27169 256.80774 427.73563 170.04542 113.41537 226.67548 14.018976 11.290384 16.74757 101.92211 NA 90.10999 113.73424 115.56990 99.46147 131.67834 1.197007 1.0662985 1.327715
223 Central Interior Broadleaf Forest east 6388 3194 0.8461273 0.0146625 0.6087525 1.0835021 0.7112156 0.0011445 0.6448959 0.7775352 127.11413 118.06312 136.16514 37.02397 34.56160 39.48633 17.800944 13.742432 21.85946 98.51432 NA 90.85761 106.17104 113.18502 99.49412 126.87591 1.445696 1.2995960 1.591796
231 Southeastern Mixed Forest east 7790 3895 1.4759858 0.0331065 1.1193112 1.8326605 0.6508476 0.0005086 0.6066399 0.6950552 144.97930 132.73182 157.22678 30.16077 27.76581 32.55574 16.127853 14.505323 17.75038 120.36292 NA 109.42373 131.30210 112.83900 94.67141 131.00659 1.633502 1.5036347 1.763370
232 Outer Coastal Plain Mixed Forest east 7940 3970 1.0085159 0.0364082 0.6344793 1.3825526 0.7104306 0.0004570 0.6685254 0.7523358 408.34768 328.15225 488.54310 159.56714 117.80214 201.33213 20.518658 18.511922 22.52539 121.27486 NA 108.92335 133.62637 111.11452 92.96303 129.26601 1.502835 1.3689187 1.636751
234 Lower Mississippi Riverine Forest east 830 415 0.4023597 0.1697654 -0.4063858 1.2111052 0.7883253 0.0049140 0.6507290 0.9259216 395.47217 23.90610 767.03825 99.96670 -38.80593 238.73932 0.000000 -11.644423 11.64442 340.82383 NA -60.32947 741.97714 675.40707 -1170.66705 2521.48119 2.554711 1.2035154 3.905907
242 Pacific Lowland Mixed Forest west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1392 696 0.3416233 0.0635084 -0.1527370 0.8359836 0.7012428 0.0088949 0.5162318 0.8862538 142.90894 116.45330 169.36458 39.02880 31.20558 46.85201 24.394348 16.444251 32.34445 93.28179 NA 78.72633 107.83724 102.73710 85.23504 120.23915 1.135955 0.9228090 1.349101
255 Prairie Parkland (Subtropical) east 444 222 -0.2439613 0.3026388 -1.3251902 0.8372676 0.5283394 0.0248661 0.2184128 0.8382661 320.37518 110.66455 530.08580 143.22594 39.60855 246.84333 9.564518 5.735244 13.39379 88.51384 NA 63.99654 113.03113 55.99135 44.35208 67.63061 1.039193 0.8154724 1.262914
261 California Coastal Chaparral Forest and Shrub west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe west 118 59 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe west 154 77 3.0054586 17.0455900 -5.1532211 11.1641382 0.9713883 0.0886175 0.3831227 1.5596540 231.92537 -216.63238 680.48311 219.82421 -175.36661 615.01504 NA NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 66 33 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5108 2554 0.5302798 0.0245169 0.2233184 0.8372412 0.8138994 0.0007135 0.7615330 0.8662658 324.77328 285.05180 364.49475 102.66625 81.59293 123.73957 14.565033 8.704894 20.42517 155.65092 NA 135.84666 175.45518 179.79825 140.99259 218.60392 1.586471 1.3826673 1.790274
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5186 2593 0.8757158 0.0198734 0.5993491 1.1520824 0.8243016 0.0015756 0.7464844 0.9021187 162.45200 151.44589 173.45812 37.03352 34.96976 39.09727 31.761299 26.624837 36.89776 122.35089 NA 113.30935 131.39243 103.12833 95.13370 111.12296 1.273667 1.1587869 1.388547
M223 Ozark Broadleaf Forest Meadow east 602 301 -0.0785477 0.0691598 -0.5950347 0.4379392 0.8995732 0.0095032 0.7081176 1.0910287 298.68647 216.71203 380.66091 95.82372 58.74951 132.89792 NA NA NA NA NA NA NA NA NA NA NA NA NA
M231 Ouachita Mixed Forest east 680 340 0.5697483 0.2542625 -0.4203280 1.5598245 0.8582543 0.0129720 0.6346241 1.0818845 315.82677 192.43391 439.21963 147.84274 82.82219 212.86329 NA NA NA NA NA NA NA NA NA NA NA NA NA
M242 Cascade Mixed Forest west 34 17 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow west 330 165 1.8945480 1.6701111 -0.6478649 4.4369609 0.6580466 0.0763610 0.1144095 1.2016837 65.92482 39.59387 92.25577 30.81882 23.44844 38.18920 NA NA NA NA NA NA NA NA NA NA NA NA NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow west 8 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow west 22 11 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest west 306 153 0.0766154 0.4376976 -1.2253593 1.3785901 0.7782879 0.0168399 0.5229091 1.0336667 99.54181 61.69380 137.38982 53.05797 18.30561 87.81033 NA NA NA NA NA NA NA NA NA NA NA NA NA
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

parameter variance co-variance

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

plot alpha (biomass compensation effect)

plot A (asymptote of B)

## Warning: Removed 19 rows containing missing values (`geom_point()`).

plot k (stand age at half biomass asymptote)

## Warning: Removed 19 rows containing missing values (`geom_point()`).


Model Bookeeping

The model bookeeping code begins here. See the methods of the main paper for specific details, but briefly, biomass change attribution to a given driver. either: 1. changes in stand age, 2: productivity trends (as a function of measurement year), or 3: disturbance (quantified as the change in the plot fractional Biomass loss) are calculated by taking the difference between the last and first FIA plot re-measurement in the temporally-balanced dataset. For the Biomass Change (DeltaB) component in question, we use predict on the nls model varying only the given driver between the last and first re-measurement and setting the other drivers to value at the first re-measurement.

For errors in the various biomass change components, we account for model parameter uncertainty. We simulate 9999 parameter draws from the multivariate normal distribution of the nls model parameter space and predict the age function (f(x)) only using model estimates of alpha and tau in the same manner as described above.

Additional code for bookeeping model validation and plots for the supplemental information of the manuscript is contained below.

1. Set up Dataframes & Calculate Empirical Delta-B total

2. Delta-B due to Delta-STDAGE

simulate f(age) - Variance in DeltaB_age – rmvnorm

3. Delta-B due to productivity trend

simulate f(year) - Variance in DeltaB_productivity trend – rmvnorm

4. Delta-B due to disturbance

simulate f(disturbance) - Variance in DeltaB_disturbance – rmvnorm

plotting loss rate - first & last

BK_df (Bookeeping Dataframe)

BK_df avgs (Bookeeping averages by Ecoprovince)

Comparing & Checking Delta_B Model Bookeeping

compare DeltaB_oberved and DeltaB_SUM_total

## `geom_smooth()` using formula = 'y ~ x'

Delta B age vs. Delta Stand age

## `geom_smooth()` using formula = 'y ~ x'

Delta B_productivity trend vs. tau

## `geom_smooth()` using formula = 'y ~ x'

Delta B_disturbance vs. -alpha X MBL

## `geom_smooth()` using formula = 'y ~ x'

plotting Delta B

bookeping fig take 1

bookeeping fig - take 2

## Warning: Removed 15738 rows containing missing values (`geom_point()`).

### 6. stand age densities

make a fig

## Warning: package 'ggridges' was built under R version 4.2.2
## Picking joint bandwidth of 4.73
## Warning: Removed 1 rows containing non-finite values (`stat_density_ridges()`).
## Warning: Using the `size` aesthietic with geom_segment was deprecated in ggplot2 3.4.0.
## ℹ Please use the `linewidth` aesthetic instead.

Fig. 3 – combined bookeeper with stand age densities

## Picking joint bandwidth of 4.73
## Warning: Removed 1 rows containing non-finite values (`stat_density_ridges()`).

relationship of DeltaB_observed and DeltaB_productivity trend

## 
##  Pearson's product-moment correlation
## 
## data:  BK_df$DeltaB_year and BK_df$DeltaB_total
## t = -16.291, df = 31577, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.10222372 -0.08034876
## sample estimates:
##         cor 
## -0.09129725
## 
##  Pearson's product-moment correlation
## 
## data:  year_avg_merger1$value_year and year_avg_merger1$value_total
## t = 2.6013, df = 12, p-value = 0.02317
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.1025738 0.8577687
## sample estimates:
##       cor 
## 0.6004734
## `geom_smooth()` using formula = 'y ~ x'

relationship of DeltaB_observed and DeltaB_age

## 
##  Pearson's product-moment correlation
## 
## data:  BK_df$DeltaB_age and BK_df$DeltaB_total
## t = 116.95, df = 31577, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.5420054 0.5573981
## sample estimates:
##       cor 
## 0.5497484
## 
##  Pearson's product-moment correlation
## 
## data:  year_avg_merger2$value_age and year_avg_merger2$value_total
## t = 2.1683, df = 12, p-value = 0.05095
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -1.667272e-05  8.280454e-01
## sample estimates:
##       cor 
## 0.5305675
## `geom_smooth()` using formula = 'y ~ x'

relationship of DeltaB_observed and DeltaB_disturbance

## 
##  Pearson's product-moment correlation
## 
## data:  BK_df$DeltaB_disturbance and BK_df$DeltaB_total
## t = 138.31, df = 31577, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.6072941 0.6210318
## sample estimates:
##       cor 
## 0.6142095
## 
##  Pearson's product-moment correlation
## 
## data:  year_avg_merger3$value_disturbance and year_avg_merger3$value_total
## t = -0.4265, df = 12, p-value = 0.6773
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6130306  0.4366957
## sample estimates:
##        cor 
## -0.1221971
## `geom_smooth()` using formula = 'y ~ x'

## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

plotting compare Delta B altogether

## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## Warning: ggrepel: 8 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
## Warning: ggrepel: 5 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
## Warning: ggrepel: 3 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps